Chapter 7 Solutions - Oregon State University
Chapter 7 Solutions
(Problems 4, 5, 8, 9, 15, 18, and 23)
Problem #4
Current convertible preferred stock is trading at $105 with a 6% dividend rate. The straight preferred stock has a dividend yield of 0.09 (or 9%). I think the question misstated the dividend rate of the straight preferred at 9%. If this was true you would need to know the price of the straight preferred to find the yield on the straight preferred.
MAJOR ASSUMPTION – both the straight preferred and convertible preferred have the same dividend rights.
Price of the straight part of the convertible is ($100 x 0.06) / 0.09 = $66.67
If it is selling for a premium ($105) then the difference in price is the equity component (option value of the convertible preferred stock).
Option Value = $105 - $66.67 = $38.33
Problem #5
Missing data – bond is a ten year bond.
Start again with a major assumption that the straight bond and the convertible bond would sell for the same yield.
Again find the value of the straight component of the convertible bond…
Easy way is via TVM keys on a calculator
Assume semi-annual bond (because most are and the author does not mention it for these bonds)
Coupon Payments are: 0.05 x $1,000 / 2 = $25
Set P/Y = 2 and C/Y =2
Input 20 8.0 ? 25.00 1,000.00
N I/Y PV PMT FV
CPT 796.15
Now if the straight portion of the bond is worth $796.15 and the bond is selling for $1,100.00 then the option value of the conversion feature is worth
$1,100 -$796.15 = $303.85
We can “classify” the option value as equity (probably not done this way…)
Debt value is in two parts, $25 million in straight debt and 20,000 convertible bonds with a value of $796.15 or 15,923,000, TOTAL DEBT = $40,923,000
Equity value in two parts, 1 million shares of stock trading $50 or $50,000,000
and 20,000 convertible bonds with equity component of $303.85 or $6,077,000
TOTAL EQUITY = $56,077,000
Debt / Equity Ratio = $40,923,000 / $56,077,000 = 0.7298 or 72.98%
Debt Ratio = (Debt over Value) = $40,923 / ($40,923 + $56.077) = 0.4219 or 42.19%
Problem #8
a. Should the firm take $20,000,000 for 30% of the firm?
The new firm value after venture capital funding is $80 + $20 …where does the $120 come from? There must be some positive NPV projects that increase the value of the firm an additional $20 through the funding of projects by this new cash in-flow.
Let’s assume the firm’s value only goes to $100 million and the old owners would have the following value 0.70 x $100,000,000 = $70,000,000 so they should not sell off the 30% for $20,000,000 (unless they can use it to increase the firm value to $120 million)
Let’s now assume the firm’s value goes to $120 million and the old owners would have the following value 0.70 x $120,000,000 = $84,000,000 and it increases their wealth by $4 million (accept)
b. What is the break-even point in terms of percent of ownership?
If we stay with the $100 million final value, the percent of ownership that would leave the old owners at their $80 million is:
100 x (1 - percent sold) = 80
percent sold = 1 – (80 /100) = 1 – 80% = 20%, they should only give 20% ownership for $20 million.
If we accept the new $120 million final value, the percent of ownership that would leave the old owners at their $80 million is:
120 x (1 – percent sold) = 80
Percent sold = 1 – (80 / 120) = 1 – 0.666 = 33.33%
New owner puts in $20 million and immediately has a value of $40 million…nice return.
Problem # 9
Do the problem with a firm value target of $100 million (collecting the $20 million from the equity sale and not the venture capitalist)
Market target price is $10 for the auction. But this is 20% underpriced to get individuals to buy the stock. The “value” is really $10/ (1-0.20) = $12.50 per share.
To raise $20 million at $10 per share requires external shares of 2,000,000.
If each share is really worth $12.50 then the total number of shares outstanding and held by the original owners is:
$100,000,000 / $12.50 = 8,000,000 shares
If 2,000,000 are sold then only 6,000,000 remain for old owners,
There value is now $12.50 x 6,000,000 = 75,000,000 and they have essentially lost $5 million to the new shareholders.
Again, if this raises the value of the company to $120 million by selling $20,000,000 of stock at $10 per share (with real value of $12.50) we have the following scenario
$120,000,000 / 12.50 = 9,600,000 shares
If 2,000,000 are sold then 7,600,000 remain for old owners,
There value is now $12.50 x 7,600,000 = $95,000,000 and they have essentially gained $15 million through the selling of equity. The company gained $40 million with the $20 million equity infusion and the new shareholders had an immediate equity gain of $5 million (their underpricing).
2,000,000 x $12.50 = $25,000,000
Again, a very nice over-night return of 25% for the new shareholders.
Problem #15
Rights subscription is really a call option (a right to buy the stock at a pre-set price). Here the holder of a right must pay $25 to buy a share.
a. How many rights does it take to buy a single share?
The firm wants $100 million and so it would need to sell $100,000,000 / $25 = 4,000,000 shares. With 10,000,000 million shares currently outstanding if each share will receive a single right then it will take 2.5 rights to buy 1 share…
10,000,000 / 4,000,000 = 2.5 rights per share
b. What is the ex-rights price?
Ex-rights price per share is total equity value divided by total shares
($50 x 10,000,000 + $25 x 4,000,000) / 14,000,000 = $42.85714286 ≈ $42.86
c. Estimate the value per right.
Pre-rights price is the difference between the value of the stock before the rights offering and the price of the stock after the rights offering
$50 - $42.85714286= $7.14285714 ≈ $7.14
Note, if the company distributed the 10,000,000 rights to the old shareholders and they are worth “$7.14” per right, the old shareholder can sell these rights to someone else at the $7.14 value per
Example, old shareholder with 100 shares before rights offering.
Value of wealth before rights offering is 100 x $50 = $5,000
Value of wealth after rights offering (receives 100 rights and can buy 40 additional shares at $25 and exercises his/her rights…
New wealth after rights offering is completed is
140 shares x $42.85714286 = $6,000
Cost of new shares is
40 x $25 = $1,000
Net new wealth is $6,000 - $1,000 = $5,000 (no change)
What if the old owner does not want to buy any more shares and sells the 100 rights that can buy 40 shares?
Revenue: 100 x $7.14285714= $714.29
New Value in stock = 100 x $42.85714286= $4,285.71
Total wealth = $4,285.71 + $714.29 = $5,000.00
d. How would you exploit a price above that in c? below that in c?
As with any asset, if the asset is an over-valued asset you would sell the asset and gain the difference.
What if the old owner does not want to buy any more shares and sells the 100 rights that can buy 40 shares and they are over-valued, say $8 per right?
Revenue: 100 x $8.00= $800.00
New Value in stock = 100 x $42.85714286= $4,285.71
Total wealth = $4,285.71 + $800.00 = $5,085.71
Gain in wealth is ($8.00 - $7.14285714) x 100 = $85.71
What about an undervalued asset? If that is the case you would want to buy these rights. Let’s assume they sell for $6.00 per right and you buy 100 rights and can then buy 40 shares at $25 per share:
Total cost of 40 shares,
100 x $6.00 + 40 x $25 = $600 + $1,000 = $1,600
Value of 40 shares,
40 x $42.85714286 = $1,714.285714
Gain on transaction is
$1,714.285714 - $1,600.00 = $114.29
Or (7.14285714 - $6.00) x 100 = $114.29
Problem #18
a. Annual interest tax savings on the issuing of the new debt ($40 million with interest rate of 9% and corporate tax rate of 35%)
Annual Interest Expense = $40,000,000 x 0.09 = $3,600,000
Annual Tax reduction = $3,600,000 x 0.35 = $1,260,000
You can think of it this way, the government is paying part of the interest.
Actual cost of debt is (0.09) x (1 – 0.35) = 0.0585 or 5.85%
b. Estimate the present value of the interest savings (we assume that the debt outstanding is always $40,000,000 and at 9% interest rate)
Perpetuity (forever) $1,260,000 / 0.09 = $14,000,000
Or $40,000,000 x 0.35 = $14,000,000
So the debt tax shield will usually be calculated as (Debt times tax rate)
c. If the debt has a finite life you get the $1.260,000 savings for only ten years (at 0.09 or 9%) then
PV = [pic]
d. If interest rates drop to 7% …two ways to interpret this…first and probably the most logical is to assume that the debt was issued forever at 9% or ten years at 9% and so a subsequent drop in interest rate has no bearing on the future tax shield as the firm’s obligation does not change and the tax rate does not change. Just think about an impact on a homeowner with a mortgage when interest rates change, there is not impact to the homeowner on a fixed rate loan.
A second way to view this is that the company would “re-issue” bonds or pay-off the loan and borrow at the lower 7% interest rate…now just redo everything at 7% for the tax shield…(debt for debt swap)
Annual Interest Expense = $40,000,000 x 0.07 = $2,800,000
Annual Tax reduction = $2,800,000 x 0.35 = $980,000
Perpetuity (forever) $980,000 / 0.07 = $14,000,000
Or $40,000,000 x 0.35 = $14,000,000
PV = [pic]
Problem #23
Nadir is an unlevered firm (100% equity firm).
EBIT each year is $2,000,000
Tax rate is 40%
Market Value of the firm is $12 million.
Stock has a beta of 1 and the risk-free rate is 9% with a risk-premium of 6%.
Default free interest rate is currently 12% and present value of bankruptcy is $8 million.
a. What are the cost of equity and the WACC of the company as a 100% equity firm?
Using the SML approach we have:
E(r) = 9.0% + 1.0 (6.0%) = 15%
Using Market Value and the assumption that the firm is an on-going concern we have
Value of the firm = EBIT (1 - 0.40) / r
$12,000,000 = $2,000,000 (1 - 0.40) / r
r = $1,200,000 / $12,000,000 = 10%
How do you reconcile this? If owners want a 15% return then the value of the firm is only $8,000,000 to the current owners if the annual after-tax cash flow is $1,200,000.
b. Optimal capital structure is where the marginal benefits of the tax shield = marginal cost of bankruptcy…
Make a table for the benefits and costs…
Value of Debt Tax Shield (40%) Bankruptcy Cost x Probability Net
$2,500,000 $1,000,000 $8,000,000 x 0.0 = $0 $1,000,000
$5,000,000 $2,000,000 $8,000,000 x 0.08 = $640,000 $1,360,000
$7,500,000 $3,000,000 $8,000,000 x 0.205= $1,640,000 $1,360,000
$8,000,000 $3,200,000 $8,000,000 x 0.30 = $2,200,000 $1,200,000
$9,000,000 $3,600,000 $8,000,000 x 0.45 = $3,600,000 $0
The optimal capital structure falls between borrowing $5,000,000 and $7,500,000
c. Value of the firm at this optimal structure
Firm Value is $12,000,000 plus net tax shield of $1,360,000 = $13,360,000
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